Sign Tests for Long-memory Time Series

This paper proposes sign-based tests for simple and composite hypotheses on the long-memory parameter of a time series process. The tests allow for nonstationary hypothesis, such as unit root, as well as for stationary hypotheses, such as weak dependence or no integration. The proposed generalized Lagrange multiplier sign tests for simple hypotheses on the long-memory parameter are exact and locally optimal among those in their class. We also propose tests for composite hypotheses on the parameters of ARFIMA processes. The resulting tests statistics have a standard normal limiting distribution under the null hypothesis.Publicad

A new class of distribution-free tests for time series models specification

The construction of asymptotically distribution free time series model specification tests using as statistics the estimated residual autocorrelations is considered from a general view point. We focus our attention on Box-Pierce type tests based on the sum of squares of a few estimated residual autocorrelations. This type of tests belong to the class defined by quadratic forms of weighted residual autocorrelations, where weights are suitably transformed resulting in asymptotically distribution free tests. The weights can be optimally chosen to maximize the power function when testing in the direction of local alternatives. The optimal test in this class against MA, AR or Bloomfield alternatives is a Box-Pierce type test based on the sum of squares of a few transformed residual autocorrelations. Such transformations are, in fact, the recursive residuals in the projection of the residual autocorrelations on a certain score function

Effect of shape anisotropy on the phase diagram of the Gay-Berne fluid

We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter $3.0\leq x_0\leq 4.0$ in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows significant changes. The fluid at low temperature is found to freeze directly from isotropic to smectic A phase for all the values of $x_0$ considered by us on increasing the density while nematic phase stabilizes in between isotropic and smectic A phases only at high temperatures and densities. Both isotropic-nematic and nematic-smectic A transition density and pressure are found to decrease as we increase $x_0$. The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement.Comment: 15 pages, 6 figure

A new class of distribution-free tests for time series models specification

The construction of asymptotically distribution free time series model specification tests using as statistics the estimated residual autocorrelations is considered from a general view point. We focus our attention on Box-Pierce type tests based on the sum of squares of a few estimated residual autocorrelations. This type of tests belong to the class defined by quadratic forms of weighted residual autocorrelations, where weights are suitably transformed resulting in asymptotically distribution free tests. The weights can be optimally chosen to maximize the power function when testing in the direction of local alternatives. The optimal test in this class against MA, AR or Bloomfield alternatives is a Box-Pierce type test based on the sum of squares of a few transformed residual autocorrelations. Such transformations are, in fact, the recursive residuals in the projection of the residual autocorrelations on a certain score function.Dynamic regression model, Optimal tests, Recursive residuals, Residual autocorrelation function, Specification tests, Time series models

A new class of distribution-free tests for time series models specification

The construction of asymptotically distribution free time series model specification tests using as statistics the estimated residual autocorrelations is considered from a general view point. We focus our attention on Box-Pierce type tests based on the sum of squares of a few estimated residual autocorrelations. This type of tests belongs to the class defined by quadratic forms of weighted residual autocorrelations, where weights are suitably transformed resulting in asymptotically distribution free tests. The weights can be optimally chosen to maximize the power function when testing in the direction of local alternatives. The optimal test in this class against MA, AR or Bloomfield alternatives is a Box-Pierce type test based on the sum of squares of a few transformed residual autocorrelations. Such transformations are, in fact, the recursive residuals in the projection of the residual autocorrelations on a certain score function.

A new class of distribution-free tests for time series models specification

The construction of asymptotically distribution free time series model specification tests using as statistics the estimated residual autocorrelations is considered from a general view point. We focus our attention on Box-Pierce type tests based on the sum of squares of a few estimated residual autocorrelations. This type of tests belongs to the class defined by quadratic forms of weighted residual autocorrelations, where weights are suitably transformed resulting in asymptotically distribution free tests. The weights can be optimally chosen to maximize the power function when testing in the direction of local alternatives. The optimal test in this class against MA, AR or Bloomfield alternatives is a Box-Pierce type test based on the sum of squares of a few transformed residual autocorrelations. Such transformations are, in fact, the recursive residuals in the projection of the residual autocorrelations on a certain score function

Liquid-crystal patterns of rectangular particles in a square nanocavity

Using density-functional theory in the restricted-orientation approximation, we analyse the liquid-crystal patterns and phase behaviour of a fluid of hard rectangular particles confined in a two-dimensional square nanocavity of side length $H$ composed of hard inner walls. Patterning in the cavity is governed by surface-induced order, capillary and frustration effects, and depends on the relative values of particle aspect ratio $\kappa\equiv L/\sigma$, with $L$ the length and $\sigma$ the width of the rectangles ($L\ge\sigma$), and cavity size $H$. Ordering may be very different from bulk ($H\to\infty$) behaviour when $H$ is a few times the particle length $L$ (nanocavity). Bulk and confinement properties are obtained for the cases $\kappa=1$, 3 and 6. In the confined fluid surface-induced frustration leads to four-fold symmetry breaking in all phases (which become two-fold symmetric). Since no director distorsion can arise in our model by construction, frustration in the director orientation is relaxed by the creation of domain walls (where the director changes by $90^{\circ}$); this configuration is necessary to stabilise periodic phases. For $\kappa=1$ the crystal becomes stable with commensuration transitions taking place as $H$ is varied. In the case $\kappa=3$ the commensuration transitions involve columnar phases with different number of columns. Finally, in the case $\kappa=6$, the high-density region of the phase diagram is dominated by commensuration transitions between smectic structures; at lower densities there is a symmetry-breaking isotropic $\to$ nematic transition exhibiting non-monotonic behaviour with cavity size.Comment: 31 pages, 15 figure

Distribution Free Goodness-of-Fit Tests for Linear Processes

This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals of a (approximated) martingale transformation of the Bartlett's Tp-process with estimated parameters, which converges in distribution to the standard Brownian Motion under the null hypothesis. We discuss tests of different nature such as omnibus, directional and Portmanteau-type tests. A Monte Carlo study illustrates the performance of the different tests in practice.Nonparametric model checking, spectral distribution, linear processes, martingale decomposition, local alternatives, omnibus, smooth and directional tests, long-range alternatives

Methods and metrics for the improvement of the interaction and the rehabilitation of cerebral palsy through inertial technology

Cerebral palsy (CP) is one of the most limiting disabilities in childhood, with 2.2 cases per 1000 1-year survivors. It is a disorder of movement and posture due to a defect or lesion of the immature brain during the pregnancy or the birth. These motor limitations appear frequently in combination with sensory and cognitive alterations generally result in great difficulties for some people with CP to manipulate objects, communicate and interact with their environment, as well as limiting their mobility. Over the last decades, instruments such as personal computers have become a popular tool to overcome some of the motor limitations and promote neural plasticity, especially during childhood. According to some estimations, 65% of youths with CP that present severely limited manipulation skills cannot use standard mice nor keyboards. Unfortunately, even when people with CP use assistive technology for computer access, they face barriers that lead to the use of typical mice, track balls or touch screens for practical reasons. Nevertheless, with the proper customization, novel developments of alternative input devices such as head mice or eye trackers can be a valuable solution for these individuals. This thesis presents a collection of novel mapping functions and facilitation algorithms that were proposed and designed to ease the act of pointing to graphical elements on the screen—the most elemental task in human-computer interaction—to individuals with CP. These developments were implemented to be used with any head mouse, although they were all tested with the ENLAZA, an inertial interface. The development of such techniques required the following approach: Developing a methodology to evaluate the performance of individuals with CP in pointing tasks, which are usually described as two sequential subtasks: navigation and targeting. Identifying the main motor abnormalities that are present in individuals with CP as well as assessing the compliance of these people with standard motor behaviour models such as Fitts’ law. Designing and validating three novel pointing facilitation techniques to be implemented in a head mouse. They were conceived for users with CP and muscle weakness that have great difficulties to maintain their heads in a stable position. The first two algorithms consist in two novel mapping functions that aim to facilitate the navigation phase, whereas the third technique is based in gravity wells and was specially developed to facilitate the selection of elements in the screen. In parallel with the development of the facilitation techniques for the interaction process, we evaluated the feasibility of use inertial technology for the control of serious videogames as a complement to traditional rehabilitation therapies of posture and balance. The experimental validation here presented confirms that this concept could be implemented in clinical practice with good results. In summary, the works here presented prove the suitability of using inertial technology for the development of an alternative pointing device—and pointing algorithms—based on movements of the head for individuals with CP and severely limited manipulation skills and new rehabilitation therapies for the improvement of posture and balance. All the contributions were validated in collaboration with several centres specialized in CP and similar disorders and users with disability recruited in those centres.La parálisis cerebral (PC) es una de las deficiencias más limitantes de la infancia, con un incidencia de 2.2 casos por cada 1000 supervivientes tras un año de vida. La PC se manifiesta principalmente como una alteración del movimiento y la postura y es consecuencia de un defecto o lesión en el cerebro inmaduro durante el embarazo o el parto. Las limitaciones motrices suelen aparecer además en compañía de alteraciones sensoriales y cognitivas, lo que provoca por lo general grandes dificultades de movilidad, de manipulación, de relación y de interacción con el entorno. En las últimas décadas, el ordenador personal se ha extendido como herramienta para la compensación de parte de estas limitaciones motoras y como medio de promoción de la neuroplasticidad, especialmente durante la infancia. Desafortunadamente, cerca de un 65% de las personas PC que son diagnosticadas con limitaciones severas de manipulación son incapaces de utilizar ratones o teclados convencionales. A veces, ni siquiera la tecnología asistencial les resulta de utilidad ya que se encuentran con impedimentos que hacen que opten por usar dispositivos tradicionales aun sin dominar su manejo. Para estas personas, los desarrollos recientes de ratones operados a través de movimientos residuales con la cabeza o la mirada podrían ser una solución válida, siempre y cuando se personalice su manejo. Esta tesis presenta un conjunto de novedosas funciones de mapeo y algoritmos de facilitaci ón que se han propuesto y diseñado con el ánimo de ayudar a personas con PC en las tareas de apuntamiento de objetos en la pantalla —las más elementales dentro de la interacción con el ordenador. Aunque todas las contribuciones se evaluaron con la interfaz inercial ENLAZA, desarrollada igualmente en nuestro grupo, podrían ser aplicadas a cualquier ratón basado en movimientos de cabeza. El desarrollo de los trabajos se resume en las siguientes tareas abordadas: Desarrollo de una metodología para la evaluación de la habilidad de usuarios con PC en tareas de apuntamiento, que se contemplan como el encadenamiento de dos sub-tareas: navegación (alcance) y selección (clic). Identificación de los tipos de alteraciones motrices presentes en individuos con PC y el grado de ajuste de éstos a modelos estándares de comportamiento motriz como puede ser la ley de Fitts. Propuesta y validación de tres técnicas de facilitación del alcance para ser implementadas en un ratón basado en movimientos de cabeza. La facilitación se ha centrado en personas que presentan debilidad muscular y dificultades para mantener la posición de la cabeza. Mientras que los dos primeros algoritmos se centraron en facilitar la navegación, el tercero tuvo como objetivo ayudar en la selección a través de una técnica basada en pozos gravitatorios de proximidad. En paralelo al desarrollo de estos algoritmos de facilitación de la interacción, evaluamos la posibilidad de utilizar tecnología inercial para el control de videojuegos en rehabilitación. Nuestra validación experimental demostró que este concepto puede implementarse en la práctica clínica como complemento a terapias tradicionales de rehabilitación de la postura y el equilibrio. Como conclusión, los trabajos desarrollados en esta tesis vienen a constatar la idoneidad de utilizar sensores inerciales para el desarrollo de interfaces de accesso alternativo al ordenador basados en movimientos residuales de la cabeza para personas con limitaciones severas de manipulación. Esta solución se complementa con algoritmos de facilitación del alcance. Por otra parte, estas soluciones tecnológicas de interfaz con el ordenador representan igualmente un complemento de terapias tradicionales de rehabilitación de la postura y el equilibrio. Todas las contribuciones se validaron en colaboración con una serie de centros especializados en parálisis cerebral y trastornos afines contando con usuarios con discapacidad reclutados en dichos centros.This thesis was completed in the Group of Neural and Cognitive Engineering (gNEC) of the CAR UPM-CSIC with the financial support of the FP7 Framework EU Research Project ABC (EU-2012-287774), the IVANPACE Project (funded by Obra Social de Caja Cantabria, 2012-2013), and the Spanish Ministry of Economy and Competitiveness in the framework of two projects: the Interplay Project (RTC-2014-1812-1) and most recently the InterAAC Project (RTC-2015-4327-1)Programa Oficial de Doctorado en Ingeniería Eléctrica, Electrónica y AutomáticaPresidente: Juan Manuel Belda Lois.- Secretario: María Dolores Blanco Rojas.- Vocal: Luis Fernando Sánchez Sante

Distribution-free tests for time series models specification

We consider a class of time series specification tests based on quadratic forms of weighted sums of residuals autocorrelations. Asymptotically distribution-free tests in the presence of estimated parameters are obtained by suitably transforming the weights, which can be optimally chosen to maximize the power function when testing in the direction of local alternatives. We discuss in detail an asymptotically optimal distribution-free alternative to the popular Box-Pierce when testing in the direction of AR or MA alternatives. The performance of the test with small samples is studied by means of a Monte Carlo experiment.Publicad